Abstract
It has been observed that for the axially symmetric Einstein-Rosen metric, the stress-tensor of a scalar meson field associated with meson of rest mass μ cannot be the source term for generating gravitation. The above result also holds even when this meson field is coupled with an electromagnetic field.
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Roy, A.R., Rao, J.R. Non-existence of axially symmetric massive scalar fields. Commun.Math. Phys. 27, 162–166 (1972). https://doi.org/10.1007/BF01645619
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DOI: https://doi.org/10.1007/BF01645619